The fuel pump module (all in one unit) is an electric pump, it makes a interesting whine sound when first fired up and generally the engine noise will overcome that whine. For the pulsating sound, it maybe your EVAP canister clogged up. They have been known to clog up from a few other cobalt owners.
Your fuel pump filter is a strainer built on the pump module, you can clean it, but it should not generally give out or clog up within the first year. My strongest suggestion for you is to pull out your spark plugs and you can see if your burning correctly the right amount of fuel. If it shows lean condition on the plugs, you should be able to take back your fuel pump unit and with the recall inquiry at no cost to you.
Is your check engine light illuminated?
The reason why I say "pull out your spark plugs" is to save your grief in your combustion chamber. You can google spark plug wear indicator charts and it should pop up a bunch of pictures and a brief explanation of what each wear indicates. If its lean, then you know for a fact that your fuel system is causing the problem. Its much easier than pulling out your fuel pump module from under the back seat and finding out, that's not the problem.
2009 Cobalt LS XFE U74
Mods: K&N Typhoon Intake, Option Cat-Back Exhaust, Cosmo Short shifter, Maxxim Ahead 17X7's, MPx shorty antenna, FE5 Strut/shocks, Tein S Techs, Moog endlinks, Moog spring seaters, ZZP shorty header, LSJ downpipe, LNF front grille
Last edited by 5t3alth; 12-30-2013 at 05:25 AM.